The document NCERT Solutions Chapter 4 - Linear Equation In Two Variables (I), Class 9, Maths Class 9 Notes | EduRev is a part of Class 9 category.

All you need of Class 9 at this link: Class 9

**1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be x and that of a pen to be y).**

**Answer**

Let the cost of pen be y and the cost of notebook be x.

A/q,

Cost of a notebook = twice the pen = 2y.

âˆ´2y = x

â‡’ x - 2y = 0

This is a linear equation in two variables to represent this statement.

**2. Express the following linear equations in the form ax by c = 0 and indicate the values of a, b and c in each case: (i) 2x + 3y = 9.35 **

**(ii) x - y/5 - 10 = 0 **

**(iii) -2x + 3y = 6 **

**(iv) x = 3y**

**(v) 2x = -5y **

**(vi) 3x + 2 = 0 **

**(vii) y - 2 = 0 **

**(viii) 5 = 2x****Answer**

(i) 2x + 3y = 9.35

â‡’ 2x + 3y - 9.35 = 0

On comparing this equation with ax + by + c = 0, we get

a = 2x, b = 3 and c = -9.35

(ii) x - y/5 - 10 = 0

On comparing this equation with ax + by + c = 0, we get

a = 1, b = -1/5 and c = -10

(iii) -2x + 3y = 6

â‡’ -2x + 3y - 6 = 0

On comparing this equation with ax + by + c = 0, we get

a = -2, b = 3 and c = -6

(iv) x = 3y

â‡’ x - 3y = 0

On comparing this equation with ax + by + c = 0, we get

a = 1, b = -3 and c = 0

(v) 2x = -5y

â‡’ 2x + 5y = 0

On comparing this equation with ax + by + c = 0, we get

a = 2, b = 5 and c = 0

(vi) 3x + 2 = 0

â‡’ 3x + 0y + 2 = 0

On comparing this equation with ax + by + c = 0, we get

a = 3, b = 0 and c = 2

(vii) y - 2 = 0

â‡’ 0x + y - 2 = 0

On comparing this equation with ax + by + c = 0, we get

a = 0, b = 1 and c = -2

(viii) 5 = 2x

â‡’ -2x + 0y + 5 = 0

On comparing this equation with ax + by + c = 0, we get

a = -2, b = 0 and c = 5

**Exercise 4.2 1. Which one of the following options is true, and why? y = 3x + 5 has (i) a unique solution, **

**(ii) only two solutions, **

**(iii) infinitely many solutions****Answer**

Since the equation, y = 3x + 5 is a linear equation in two variables. It will have (iii) infinitely many solutions.**2. Write four solutions for each of the following equations: (i) 2x + y = 7 **

**(ii) Ï€x + y = 9 **

**(iii) x = 4y****Answer**

(i) 2x + y = 7

â‡’ y = 7 - 2x

â†’ Put x = 0,

y = 7 - 2 Ã— 0 â‡’ y = 7

(0, 7) is the solution.

â†’ Now, put x = 1

y = 7 - 2 Ã— 1 â‡’ y = 5

(1, 5) is the solution.

â†’ Now, put x = 2

y = 7 - 2 Ã— 2 â‡’ y = 3

(2, 3) is the solution.

â†’ Now, put x = -1

y = 7 - 2 Ã— -1 â‡’ y = 9

(-1, 9) is the solution.

The four solutions of the equation 2x + y = 7 are (0, 7), (1, 5), (2, 3) and (-1, 9).

(ii) Ï€x + y = 9

â‡’ y = 9 - Ï€x

â†’ Put x = 0,

y = 9 - Ï€Ã—0 â‡’ y = 9

(0, 9) is the solution.

â†’ Now, put x = 1

y = 9 - Ï€Ã—1 â‡’ y = 9-Ï€

(1, 9-Ï€) is the solution.

â†’ Now, put x = 2

y = 9 - Ï€Ã—2 â‡’ y = 9-2Ï€

(2, 9-2Ï€) is the solution.

â†’ Now, put x = -1

y = 9 - Ï€Ã— -1 â‡’ y = 9+Ï€

(-1, 9+Ï€) is the solution.

The four solutions of the equation Ï€x + y = 9 are (0, 9), (1, 9-Ï€), (2, 9-2Ï€) and (-1, 9+Ï€).

(iii) x = 4y

â†’ Put x = 0,

0 = 4y â‡’ y = 0

(0, 0) is the solution.

â†’ Now, put x = 1

1 = 4y â‡’ y = 1/4

(1, 1/4) is the solution.

â†’ Now, put x = 4

4 = 4y â‡’ y = 1

(4, 1) is the solution.

â†’ Now, put x = 8

8 = 4y â‡’ y = 2

(8, 2) is the solution.

The four solutions of the equation Ï€x + y = 9 are (0, 0), (1, 1/4), (4, 1) and (8, 2).

**3. Check which of the following are solutions of the equation x - 2y = 4 and which are not:**

**(i) (0, 2) **

**(ii) (2, 0) **

**(iii) (4, 0) **

**(iv) (âˆš2, 4âˆš2) **

**(v) (1, 1)****Answer**

(i) Put x = 0 and y = 2 in the equation x - 2y = 4.

0 - 2Ã—2 = 4

â‡’ -4 â‰ 4

âˆ´ (0, 2) is not a solution of the given equation.

(ii) Put x = 2 and y = 0 in the equation x - 2y = 4.

2 - 2Ã—0 = 4

â‡’ 2 â‰ 4

âˆ´ (2, 0) is not a solution of the given equation.

(iii) Put x = 4 and y = 0 in the equation x - 2y = 4.

4 - 2Ã—0 = 4

â‡’ 2 = 4

âˆ´ (4, 0) is a solution of the given equation.

(iv) Put x = âˆš2 and y = 4âˆš2 in the equation x - 2y = 4.

âˆš2 - 2Ã—4âˆš2 = 4 â‡’ âˆš2 - 8âˆš2 = 4 â‡’ âˆš2(1 - 8) = 4

â‡’ -7âˆš2 â‰ 4

âˆ´ (âˆš2, 4âˆš2) is not a solution of the given equation.

(v) Put x = 1 and y = 1 in the equation x - 2y = 4.

1 - 2Ã—1 = 4

â‡’ -1 â‰ 4

âˆ´ (1, 1) is not a solution of the given equation.

**4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. Answer**

Given equation = 2x + 3y = k

x = 2, y = 1 is the solution of the given equation.

A/q,

Putting the value of x and y in the equation, we get

2Ã—2 + 3Ã—1 = k

â‡’ k = 4 + 3

â‡’ k = 7